The continuing discoveries of non-coding RNAs (ncRNAs) and their critical roles in cellular and viral machinery are inspiring novel antibacterial antitumor, and antiviral therapies based on disabling or manipulating the RNAs involved. Unfortunately, our poor biophysical understanding of how RNAs work hinders the development of these potentially life-saving efforts. A critical bottleneck has been the inapplicability of crystallography, NMR, phylogenetic analysis, and current chemical methods to determine the partly ordered 3D conformations of non-coding RNAs in all their functional states. To resolve this bottleneck, we have recently invented and benchmarked a two-dimensional mutate-and-map (M2) technology. This strategy rapidly and comprehensively determines how every single mutation of an RNA perturbs the 2'-hydroxyl chemical accessibility of every other nucleotide, giving rich information on RNA secondary and tertiary structure. We aim here to more precisely reveal both canonical base pairs and pervasive A-minor tertiary interactions by coupling M2 to two additional chemistries, flavin-mononucleotide-induced photo-oxidation (M2-FMN) and dimethyl-sulfate alkylation (M2-DMS). We propose a high-throughput M2-rescue approach to validate the resulting inferences through surgical double-mutant/rescue experiments. Finally, we will apply these technologies to determine structures of mysterious states and regions in two paradigmatic systems in RNA biophysics, the add adenine-binding riboswitch and the FN double-glycine riboswitch; this critical information is not obtainable with any other approach. We will evaluate success through benchmarks on six ncRNA domains of known structure; through M2-rescue validation; and through adoption of our methods and software tools by the broader biological community. In the same way that 2D spectroscopy transformed NMR approaches to small biomolecule structure, we propose that 2D mutate-and-map technology will transform our understanding of structure in long non-coding RNAs, full-length RNA messages, and entire retroviral genomes targeted for biomedical activation or disruption.